Issue |
A&A
Volume 510, February 2010
|
|
---|---|---|
Article Number | L6 | |
Number of page(s) | 4 | |
Section | Letters | |
DOI | https://doi.org/10.1051/0004-6361/200913893 | |
Published online | 18 February 2010 |
LETTER TO THE EDITOR
Imprints of coronal temperature disturbances on type III bursts
B. Li - I. H. Cairns - P. A. Robinson
School of Physics, University of Sydney, New South Wales 2006, Australia
Received 17 December 2009 / Accepted 29 January 2010
Abstract
The electron temperature
and ion temperature
in the corona vary with time and location, due to transient and
persistent activity on the Sun. The effects of spatially localized
disturbances in
and
on coronal type III radio bursts are simulated. The disturbances
are superimposed on monotonically varying temperature backgrounds
and arise from spatially confined solar activity, Qualitatively and
quantitatively different imprints are found on the curve of the maximum
flux versus frequency of type III bursts, because of the
disturbances in
and
.
The results indicate that nonthermal coronal type III bursts offer
a new tool to probe and distinguish between spatially localized
structures of
and
along the paths of type III beams. Furthermore, localized
temperature disturbances may be responsible for some fine structures in
type III bursts, e.g., striae in type IIIb bursts in the
presence of multiple, localized temperature disturbances.
Key words: Sun: radio radiation - Sun: corona - methods: numerical
1 Introduction
The solar corona is highly dynamic and activity occurs both impulsively
and continuously from small to large scales (e.g., microflares and
flares). The activity results in energy injection and heat transfer,
and so spatiotemporal variations in the temperature
and density
of electrons, and the ion temperature
.
For instance, spatially confined activity such as X-ray bright
points may result in multiple, spatially localized disturbances in
and
,
as in Fig. 1.
These may remain distinct from each other because tangential
discontinuities can separate different thermal plasmas for long
periods. In addition,
disturbances may be more localized and last much longer than
disturbances,
because ions have much lower thermal speeds than electrons. Knowledge
of the spatial profiles of coronal temperatures is usually obtained by
using visible, UV, X-ray, and thermal radio emission.
This knowledge, currently inadequate, is vital to understanding
coronal heating and solar wind acceleration.
![]() |
Figure 1: Illustration of the production of localized regions with enhanced coronal temperatures in an open magnetic flux tube, through which a type III beam propagates (viewed from above the north pole). Localized regions R1-R3 are caused by three separate episodes of activity at localized solar source, with the latest activity producing R3. For clarity, the flux tube is assumed to have a regular spiral shape. |
Open with DEXTER |
Type III solar radio bursts are produced when energetic electrons
accelerated in flares propagate as beams along open magnetic field
lines into the interplanetary (IP) medium, and drive Langmuir (L) waves near the electron plasma frequency
and radiation near
and/or
.
Coronal type IIIs are one of the most important diagnostics of
electron acceleration in flares and coronal conditions (Aschwanden 2002,2006).
For example, coronal type IIIs have been used to extract the
Sun's density profile, and solar-wind-like regions with
are found to be common below
,
where
is the solar radius (Cairns et al. 2009).
Sometimes, fine and/or sudden intensity changes in coronal type IIIs are observed (Fomichev & Chertok 1977; Suzuki & Dulk 1985). For example, type IIIb (stria) bursts show non-smooth variations in flux versus frequency, and chains of narrow-band structures are caused by successive modulations in flux (de La Noe & Boischot 1972). It has been variously conjectured that the flux modulations in type IIIb bursts occur because of modulational instability related to the dynamics of beam and L waves (Smith & de La Noe 1976), or filamentary coronal density structures (Takakura & Yousef 1975).
The primary aim of this letter is to demonstrate numerically the effects on coronal type IIIs
of spatially localized disturbances of
and
.
Our simulations show that
the dynamic spectrum of
emission is modulated at frequencies corresponding to the disturbances; so is the
emission, although the predictions are generally below observable levels. Importantly, distinct imprints of the
and
disturbances
exist on the curve of the maximum flux versus frequency for the
emission.
The second aim is to show that detailed structures in coronal
type IIIs can be used to probe and ideally differentiate between
localized variations of
and
along the beam path.
Fine structures resembling those in type IIIb bursts are produced
by multiple temperature disturbances, which suggests that localized
temperature disturbances may lead to type IIIb bursts.
2 Numerical model
The spatial variation in the ion temperature is defined by
at time t=0, where x
is along the radial direction and represents the distance above the
photosphere. Since we assume that ions remain Maxwellian and unchanged
during the simulations, as in our earlier work (Li et al. 2008a,2008b),
retains
its original profile at all times. However, for an inhomogeneous plasma
with position-dependent electron temperature
and/or density
,
a source term needs to be added to the kinetic equation for electrons
to preserve the given
and
profiles
for simulation periods longer than the propagation time of a beam
traversing the simulation domain. The requirement to have a source term
arises because we allow electrons to evolve dynamically. Specifically,
the electron distribution function
evolves following (Li et al. 2002):
where v denotes electron speed. The first and second terms on the right-hand side (r.h.s.) of Eq. (1) represent spontaneous and induced emission, respectively, and the coefficient D describes the coupling between the beam and L waves. The density is given by

Under thermal and steady state conditions,
is Maxwellian and given by
,
where
is the electron mass. The r.h.s. of Eq. (1) then vanishes because of the self-consistent definitions of A and D (Li et al. 2002). However, the left-hand side (l.h.s.) of Eq. (1) reduces to the advection term
,
which is non-vanishing for plasmas with x-dependent
and/or
.
So a source term is required for Eq. (1) to remain self-consistent. We thus add a source term S(x,v) to the r.h.s. of Eq. (1), and set
where



We consider first the case in which the plasma has varying
but uniform
,
for which only the first term of Eq. (3) remains. For
monotonically increasing (decreasing) with increasing x, S>0 (S<0) for electrons with v>0, and so acts as a source (sink). In contrast, S is a sink (source) for electrons with v<0.
The physics of the case when
decreases monotonically is as follows. On the one hand, for v>0
more electrons move into rather than out of a given coronal layer
during a finite time interval. Thus, to maintain the given
and
profiles a sink is needed to remove the excess electrons. On the other hand, for v<0
more electrons move out of than into the given layer,
so a source is required to supply the electrons lost because
of the imbalance.
When
is nonuniform but
is homogeneous, only the second term of Eq. (3) remains. The nature (source or sink) of the S term now depends on both the trend of the
profile and the electron speed, via the factors
and
,
respectively. If we assume that
monotonically increases with x, then at a given coronal layer statistically more electrons with
move outward rather than inward. To maintain the given
and
profiles, a source is therefore needed to supply the loss of electrons caused by the imbalance.
In contrast, at the same layer more slow electrons with
move in rather than out, thus the excess electrons need to be drained away to retain the balance.
In general, both terms in Eq. (3) remain for arbitrary, inhomogeneous profiles of
and
.
In the corona various effects may contribute to the source S.
For instance, small-scale activity, e.g., jets, can heat and
transport electrons between different locations, causing either gain or
loss of electrons at these locations.
The simulations of coronal type IIIs use here our quasilinear-based model for plasma emission (Li et al. 2008a,2008b). The model includes a 3D source region with stratified 2D layers that vary with x, the dynamics of beam, L, ion-sound (S), and transverse waves coupled via quasilinear and nonlinear processes, and radiation propagation from the source to a remote observer. The model is generalized by including the term S in Eq. (1) which allows us to study the effects of localized temperature variations.
3 Simulation results
We assume that the coronal temperatures follow
where




![]() |
Figure 2:
Spatial profiles of |
Open with DEXTER |
Figure 2 shows the spatial profiles of
and
in the simulations.
Four different temperature conditions are considered: (
)
both
and
decrease monotonically; (
)
a localized
disturbance is imposed on the background
in
,
and
is as in
;
(
) a localized
disturbance is imposed on the background
in
,
and
is as in
;
(
) three localized
disturbances are added to the background
in
,
and
is as in
.
We assume that
MK for case
,
which is much higher than the value of
MK for cases
and
.
The Tls parametrization is based upon observations (e.g., Kohl et al. 1996), which show much higher coronal proton temperatures than
,
reaching 4-6 MK or higher at height
.
Here we choose a higher
than observed so far to demonstrate clearly the effects of
localization.
We assume the 10-fold Baumbach-Allen model (Baumbach 1937; Allen 1947) for ,
and Fig. 2 also shows the resulting
profile. The acceleration of electrons during flares is represented by adding a heating term H (Robinson & Benz 2000; Li et al. 2002) to the r.h.s. of Eq. (1):
.
Here a fraction
of electrons are heated from
to
(
)
over a typical region (
,
)
centered at (
,
). Based on observations (Aschwanden 2002; Klein et al. 2005), we choose
,
MK,
ms,
ms,
Gm, and
Mm. Other simulation parameters are as in Li et al. (2008a).
Figures 3 and 4 show the dynamic spectrum of
emission at Earth and the corresponding maximum flux
versus frequency f, respectively, under the four different temperature conditions in Fig. 2. The
emission (not shown) is too weak, with flux
solar flux unit (sfu) =
,
to be observable
except for cases
and
.
This is due primarily to strong free-free absorption, strong
radiation loss by scattering, and weak source emission (Robinson &
Benz 2000; Li et al. 2008a). Below we discuss mainly the
results.
![]() |
Figure 3:
Simulated
|
Open with DEXTER |
![]() |
Figure 4:
Maximum
|
Open with DEXTER |
First, Figs. 3a and 4 (black curve) show that for case
the spectrum varies smoothly, and
decreases with f
after radiation onset, respectively. These properties and other
spectral characteristics, e.g., drift rate (not shown), agree
quantitatively with typical observations, as in our previous work
(Li et al. 2008a).
Figure 3b shows the
spectrum for case
.
The spectrum is modulated
at f corresponding to the
disturbance, and the flux is suppressed close to the center of the disturbance. Figure 4 (green curve) illustrates fine structures in
caused by the disturbance. Specifically, as f varies from high to low frequencies
varies according to the sequence ``same
decrease
increase
same'', relative to case
.
In addition,
is modulated within the range
MHz, corresponding to the disturbed region between
and
.
Furthermore,
reaches a local minimum and maximum at
MHz
MHz and
MHz, decreasing and increasing by factors of
and
relative to case
,
respectively.
Physically, on entering the region with increasing ,
the beam becomes relatively narrower and slightly faster because
extends to higher v. This causes the weaker growth of L waves, mainly because less free energy is available, although the collisional damping rate (
)
of L waves decreases slightly (Li et al. 2008b). The source
emission
is thus weaker, so is the remote radiation, although loss by
free-free absorption is reduced locally because
increases. On passing the central region of the disturbance, the beam becomes relatively wider and slower because
decreases.
The combined effects of more free energy now being available and the lower collisional damping rate result in stronger L waves, and so stronger source
emission.
Remote radiation is further strongly enhanced because of the locally
weaker free-free absorption. On exiting the disturbed region,
the beam, source waves, and radiation recover their properties for
case
.
Figure 3c shows the
spectrum for case
with a single localized
disturbance. The spectrum appears qualitatively similar to that in Fig. 3b in terms of spectral modulation. However, detailed examination of the variation in
versus f in Fig. 4 (red curve) shows both qualitative and quantitative differences and similarities exist relative to case
,
as follows:
- 1.
- The sequence of
versus f from high to low frequencies relative to case
is ``same
increase
decrease
increase
same'', which is distinct from that for case
.
- 2.
- The frequencies
MHz and 154 MHz of the two local peaks, and
MHz at the center of the local dip differ evidently from, and is quantitatively similar to, those of the single peak and trough for case
, respectively.
- 3.
- The quantitative modulation effects on
caused by the
disturbance are weaker than those caused by the
disturbance. For instance,
increases by a factor
at the two local peaks relative to case
. This factor is smaller than the factor
for case
, where
increases locally by
, while
here increases locally by a factor
.
- 4.
- The frequency region of the
modulation is basically the same as for case
.







The trend of
versus f for case
in Fig. 4 is caused by the following. As the beam enters the region where
increases, the product L waves become stronger because of the stronger ES decay, leading to stronger
source emission (produced by coupling between primary and product L waves), hence stronger remote emission (Li et al. 2005). However, as
increases further, the level of primary L waves decreases because the even stronger decay process transfer the primary L wave energy into the product L waves (Li et al. 2003). The forward-directed (anti-Sunward) emission is thus weaker. Consequently, a local dip in
appears at frequencies corresponding to where
maximizes. In the simulations, we neglected the backward-directed
emission, which is generated by coupling between product L waves (Li et al. 2008a). In general, the backward emission contributes negligibly to
because
the radiation is partly lost and time-delayed by strong scattering and
reflection closer to the Sun and undergoes additional free-free
absorption before reaching the observer, although it may affect the
temporal profile of the
flux (Riddle 1974). As the beam propagates further,
decreases, leading to relatively stronger coupling between the primary and product L waves,
and thus stronger forward
emission and higher values of
.
Once the beam passes the disturbed region, the source waves and remote radiation regain the properties for case
.
We also found (not shown) for case
that the flux of
emission is significantly enhanced (
sfu) above the thermal level and may be observable as a microburst (Kundu et al. 1986) at frequencies corresponding to the disturbance. This occurs mainly because the S waves are stronger and the
emission rate is higher for higher
.
Finally, Figs. 3d and 4 (blue curve) show the
spectrum and
versus f, respectively, for case
.
We see that the spectrum is repeatedly modulated, each modulation resembling that in Fig. 3b. Furthermore, the variations in
versus f clearly show the same signature for each
disturbance
as found for case
.
Thus, the signature of
variations with f for a single
disturbance is robust. Figure 4 also shows that greater disturbances in
relative to the background lead to qualitatively greater modulations in
(cf., the peak
values for the first and third
disturbances). Similar results are found for multiple
disturbances (not shown).
4 Discussion and conclusions
We have developed the first simulations to study the effects on coronal
type IIIs of spatially localized disturbances in
or
.
The disturbances may be produced by various coronal activities, so the simulations are more realistic than previous work.
The simulations demonstrate that the dynamic spectrum and the curve of maximum flux
versus frequency f for
emission are modulated by the
or
disturbances. Crucially, the modulation fine structures differ for
and
disturbances, both qualitatively and quantitatively. A localized increase in
produces a signature of ``trough
peak'' in the
versus f curve, while a ``peak
trough
peak'' signature occurs for a localized increase in
.
The different signatures are robust and independent of the details of the disturbances. Thus, localized
and
disturbances leave identifiable imprints on
emission. In addition, weak
emission may be observable for sufficiently large
disturbances.
One implication is that the detailed frequency fine structures in
coronal type IIIs can be used to probe and differentiate between
the localized profiles of
and
.
Thus nonthermal coronal type IIIs offer a new tool to remotely diagnose
spatial temperature structures in the corona.
We also found that larger disturbances in
or
relative to the background results in qualitatively larger amplitude modulations in
.
Furthermore, for the same disturbance in temperature the modulation effects on
are more pronounced for
than for
,
as suggested by Fig. 4.
The modulations in
spectrum caused by multiple
or
disturbances
resemble qualitatively the fine structures in
type IIIb bursts. Thus, our results suggest that localized
disturbances in
or
may produce type IIIs with striae and modulations in f. This mechanism differs from those previously proposed, e.g., modulational instability (Smith & de La Noe 1976) or filamentary density structures (Takakura & Yousef 1975).
The flux modulation mechanism here may also apply to type III beams that cross shocks. MacDowall (1989)
observed that the flux of IP type IIIs changed suddenly as
beams neared shocks. He suggested that the changes are caused by
the scattering of beam electrons by magnetic turbulence. We propose,
instead, that the heating of electrons and ions just downstream of the
shocks produces localized increases in
and
,
and so modulations in flux.
The Australian Research Council supported this work.
References
- Allen, C. W. 1947, MNRAS, 107, 426 [NASA ADS] [Google Scholar]
- Aschwanden, M. J. 2002, Space Sci. Rev., 101, 1 [NASA ADS] [CrossRef] [Google Scholar]
- Aschwanden, M. J. 2006, Physics of the Solar Corona: An Introduction with Problems and Solutions (Springer, Berlin), Chapter 15 [Google Scholar]
- Baumbach, S. 1937, Astron. Nachr., 263, 131 [Google Scholar]
- Cairns, I. H., Lobzin, V. V., Warmuth, A., et al. 2009, ApJ, 706, L265 [NASA ADS] [CrossRef] [Google Scholar]
- de La Noe, J., & Boischot, A. 1972, A&A, 20, 55 [NASA ADS] [Google Scholar]
- Fomichev, V. V., & Chertok, I. M. 1977, Radiophys. Quantum Electron., 20, 869 [NASA ADS] [CrossRef] [Google Scholar]
- Klein, K.-L., Krucker, S., Trottet, G., & Hoang, S. 2005, A&A, 431, 1047 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
- Kohl, J. L., Strachan, L., & Gardner, L. D. 1996, ApJ, 465, L141 [NASA ADS] [CrossRef] [Google Scholar]
- Kundu, M. R., Gergely, T. E., Szabo, A., Loiacono, R., & White, S. M. 1986, ApJ, 308, 436 [NASA ADS] [CrossRef] [Google Scholar]
- Li, B., Robinson, P. A., & Cairns, I. H. 2002, Phys. Plasmas, 9, 2976 [NASA ADS] [CrossRef] [Google Scholar]
- Li, B., Willes, A. J., Robinson, P. A., & Cairns, I. H. 2003, Phys. Plasmas, 10, 2748 [NASA ADS] [CrossRef] [Google Scholar]
- Li, B., Willes, A. J., Robinson, P. A., & Cairns, I. H. 2005, Phys. Plasmas, 12, 012103; 052324 [NASA ADS] [CrossRef] [Google Scholar]
- Li, B., Cairns, I. H., & Robinson, P. A. 2008a, J. Geophys. Res., 113, A06104, A06105 [Google Scholar]
- Li, B., Robinson, P. A., & Cairns, I. H. 2008b, J. Geophys. Res., A10101 [Google Scholar]
- MacDowall, R. J. 1989, Geophys. Res. Lett., 16, 923 [NASA ADS] [CrossRef] [Google Scholar]
- Parker, E. N. 2007, in Handbook of the Solar-Terrestrial Environment, ed. Y. Kamide, & A. Chian (Springer, Berlin), 95 [Google Scholar]
- Riddle, A. C. 1974, Sol. Phys., 35, 153 [NASA ADS] [CrossRef] [Google Scholar]
- Robinson, P. A., & Benz, A. O. 2000, Sol. Phys., 194, 345 [Google Scholar]
- Smith, R. A., & de La Noe, J. 1976, ApJ, 207, 605 [NASA ADS] [CrossRef] [Google Scholar]
- Suzuki, S., & Dulk, G. A. 1985, in Solar Radiophysics, ed. D. J. McLean, & N. R. Labrum (Cambridge: Cambridge Univ. Press), 289 [Google Scholar]
- Takakura, T., & Yousef, S. 1975, Sol. Phys., 40, 421 [NASA ADS] [CrossRef] [Google Scholar]
All Figures
![]() |
Figure 1: Illustration of the production of localized regions with enhanced coronal temperatures in an open magnetic flux tube, through which a type III beam propagates (viewed from above the north pole). Localized regions R1-R3 are caused by three separate episodes of activity at localized solar source, with the latest activity producing R3. For clarity, the flux tube is assumed to have a regular spiral shape. |
Open with DEXTER | |
In the text |
![]() |
Figure 2:
Spatial profiles of |
Open with DEXTER | |
In the text |
![]() |
Figure 3:
Simulated
|
Open with DEXTER | |
In the text |
![]() |
Figure 4:
Maximum
|
Open with DEXTER | |
In the text |
Copyright ESO 2010
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.